This is a moderate-sized undertaking, and does involve some on-going work to maintain. Put another way, is part of your goal here to learn about installing and maintaining a server and OS X Server, or is your foremost goal to host shared data? Running a server is an investment, both in terms of what you'll learn, as well as the hardware and the cost of the (usually) static IP network connection typically used with remotely-accessed servers.
For learning about Server.app in general, start with the Apple documentation . That'll give you some idea of what's involved, and what options are available within OS X Server.
To host services externally, you'll usually want static IP (particularly if you want mail services, and don't want to relay your mail through another host), a correct public DNS translation for your server, a network device that provides NAT (can be an AirPort or Time Capsule, but those are fairly limited for a server-oriented network), private DNS on the NAT'd network (this cannot be skipped, and simply referencing the ISP DNS services won't work with a server on a NAT'd network), and you'll also learn rather more familiar with IP networking and devices in general.
For security, you may also want to learn about a VPN, as open services tend to be probed by various folks. Establishing a VPN secures typical access into the server, and avoids the need to open up various ports to the 'net. Less stuff for folks to attack, in other words, and less stuff that you have to maintain entirely securely. (Down-revision tools and services do tend to get attacked.)
Now the far more interesting part of this request is the iCloud bit. If you really want that — services beyond calendar, mail and web and the rest of what Server.app provides — then you'll need to acquire and load more software, and quite possibly integrating that. Maybe OwnCloud or Cozy (but you'll have to get those working with OS X Server), or some other alternative.
Depending on exactly what you want your clients to be able to access and share here, there can be other alternatives and other requirements, too.
Alternatively, you can host these services at various providers. Google and other entities offer app hosting as well as dedicated hosting and other services.
Running a server for remote access is a deceptively large discussion area, so if you have particular interests or details or requirements, post away and somebody might be able to provide some more information for you.
